Multisensor thiết bị đo đạc thiết kế 6o (P4)

LINEAR SIGNAL CONDITIONING TO SIX-SIGMA CONFIDENCE
INTRODUCTION Economic considerations are imposing increased accountability on the design of analog I/O systems to provide performance at the required accuracy for computerintegrated measurement and control instrumentation without the costs of overdesign. Within that context, this chapter provides the development of signal acquisition and conditioning circuits, and derives a unified method for representing and upgrading the quality of instrumentation signals between sensors and data-conversion systems....

76 LINEAR SIGNAL CONDITIONING TO SIX-SIGMA CONFIDENCE
FIGURE 4-1. Signal conditioning design influences.
tions are outlined for contributing to the goal of minimum total instrumentation er-
ror. Sensor choices appropriate for measurands of interest were introduced in Chap-
ter 1, including linearization and calibration issues. Application-specific amplifier
and filter choices for signal conditioning are defined, respectively, in Chapters 2
and 3. In this section, input circuit noise, impedance, and grounding effects are de-
scribed for signal conditioning optimization. The following section derives models
that combine device and system quantities in the evaluation and improvement of
signal quality, expressed as total error, including the influence of random and co-
herent interference. The remaining sections provide detailed examples of these sig-
nal conditioning design methods.
External interference entering low-level instrumentation circuits frequently is
substantial and techniques for its attenuation are essential. Noise coupled to signal
cables and power buses has as its cause electric and magnetic field sources. For ex-
ample, signal cables will couple 1 mV of interference per kilowatt of 60 Hz load for
each lineal foot of cable run of 1 ft spacing from adjacent power cables. Most inter-
ference results from near-field sources, primarily electric fields, whereby an effec-
tive attenuation mechanism is reflection by nonmagnetic materials such as copper
or aluminum shielding. Both foil and braided shielded twinax signal cable offer at-
tenuation on the order of –90 voltage dB to 60 Hz interference, which degrades by
approximately +20 dB per decade of increasing frequency.

4-1 SIGNAL CONDITIONING INPUT CONSIDERATIONS 77
For magnetic fields absorption is the effective attenuation mechanism requiring
steel or mu metal shielding. Magnetic fields are more difficult to shield than electric
fields, where shielding effectiveness for a specific thickness diminishes with de-
creasing frequency. For example, steel at 60 Hz provides interference attenuation
on the order of –30 voltage dB per 100 mils of thickness. Applications requiring
magnetic shielding are usually implemented by the installation of signal cables in
steel conduit of the necessary wall thickness. Additional magnetic field attenuation
is furnished by periodic transposition of twisted-pair signal cable, provided no sig-
nal returns are on the shield, where low-capacitance cabling is preferable. Mutual
coupling between computer data acquisition system elements, for example from fi-
nite ground impedances shared among different circuits, also can be significant,
with noise amplitudes equivalent to 50 mV at signal inputs. Such coupling is mini-
mized by separating analog and digital circuit grounds into separate returns to a
common low-impedance chassis star-point termination, as illustrated in Figure 4-3.
The goal of shield ground placement in all cases is to provide a barrier between
signal cables and external interference from sensors to their amplifier inputs. Signal
cable shields also are grounded at a single point, below 1 MHz signal bandwidths,
and ideally at the source of greatest interference, where provision of the lowest im-
pedance ground is most beneficial. One instance in which a shield is not grounded
is when driven by an amplifier guard. Guarding neutralizes cable-to-shield capaci-
tance imbalance by driving the shield with common-mode interference appearing
on the signal leads; this also is known as active shielding.
The components of total input noise may be divided into external contributions
associated with the sensor circuit, and internal amplifier noise sources referred to its
input. We shall consider the combination of these noise components in the context
of band-limited sensor–amplifier signal acquisition circuits. Phenomena associated
with the measurement of a quantity frequently involve energy–matter interactions
that result in additive noise. Thermal noise Vt is present in all elements containing
resistance above absolute zero temperature. Equation (4-1) defines thermal noise
voltage proportional to the square root of the product of the source resistance and its
temperature. This equation is also known as the Johnson formula, which is typically
evaluated at room temperature or 293°K and represented as a voltage generator in
series with a noiseless source resistance.
Vt = 4kTRsVrms/ Hz
k = Boltzmann’s constant (1.38 × 10–23 J/°K) (4-1)
T = absolute temperature (°K)
Rs = source resistance ( )
Thermal noise is not influenced by current flow through its associated resistance.
However, a dc current flow in a sensor loop may encounter a barrier at any contact
or junction connection that can result in contact noise owing to fluctuating conduc-
tivity effects. This noise component has a unique characteristic that varies as the re-
ciprocal of signal frequency 1/f, but is directly proportional to the value of dc cur-

78 LINEAR SIGNAL CONDITIONING TO SIX-SIGMA CONFIDENCE
rent. The behavior of this fluctuation with respect to a sensor loop source resistance
is to produce a contact noise voltage whose magnitude may be estimated at a signal
frequency of interest by the empirical relationship of equation (4-2). An important
conclusion is that dc current flow should be minimized in the excitation of sensor
circuits, especially for low signal frequencies.
Idc
Vc = (0.57 × 10–9) Rs V / Hz (4-2)
f rms
Idc = average dc current (A)
f = signal frequency (Hz)
Rs = source resistance ( )
Instrumentation amplifier manufacturers use the method of equivalent
noise–voltage and noise–current sources applied to one input to represent internal
noise sources referred to amplifier input, as illustrated in Figure 4-2. The short-cir-
cuit rms input noise voltage Vn is the random disturbance that would appear at the
input of a noiseless amplifier, and its increase below 100 Hz is due to internal am-
plifier 1/f contact noise sources. The open circuit rms input noise current In similar-
ly arises from internal amplifier noise sources and usually may be disregarded in
sensor–amplifier circuits because its generally small magnitude typically results in
a negligible input disturbance, except when large source resistances are present.
Since all of these input noise contributions are essentially from uncorrelated
sources, they are combined as the root-sum-square by equation (4-3). Wide band-
widths and large source resistances, therefore, should be avoided in sensor–amplifi-
er signal acquisition circuits in the interest of noise minimization. Further, addition-
al noise sources encountered in an instrumentation channel following the input gain
stage are of diminished consequence because of noise amplification provided by the
input stage.
VNPP = 6.6 [(V 2 + V c + V n )( fhi)]1/2
t
2 2
(4-3)
4-2 SIGNAL QUALITY EVALUATION AND IMPROVEMENT
The acquisition of a low-level analog signal that represents some measurand, as in
Table 4-2, in the presence of appreciable interference is a frequent requirement. Of
concern is achieving a signal amplitude measurement A or phase angle at the ac-
curacy of interest through upgrading the quality of the signal by means of appropri-
ate signal conditioning circuits. Closed-form expressions are available for deter-
mining the error of a signal corrupted by random Gaussian noise or coherent
sinusoidal interference. These are expressed in terms of signal-to-noise ratios
(SNR) by equations (4-4) through (4-9). SNR is a dimensionless ratio of watts of
signal to watts of noise, and frequently is expressed as rms signal-to-interference

4-2 SIGNAL QUALITY EVALUATION AND IMPROVEMENT 81
TABLE 4-2. Signal Bandwidth Requirements
Signal Bandwidth (Hz)
dc dVs/ VFSdt
Sinusoidal 1/period T
Harmonic 10/period T
Single event 2/width
for many applications. For 95% (2 ) confidence, the error values are doubled for
the same SNR. These amplitude and phase errors are closely approximated by the
simplifications of equations (4-5) and (4-7), and are more readily evaluated than by
equations (4-4) and (4-6). For coherent interference, equations (4-8) and (4-9) ap-
proximate amplitude and phase errors where A is directly proportional to Vcoh, as
the true value of A is to VFS. Errors due to coherent interference are seen to be less
than those due to random interference by the 2 for identical SNR values. Further,
the accuracy of these analytical expressions requires minimum SNR values of one
or greater. This is usually readily achieved in practice by the associated signal con-
ditioning circuits illustrated in the examples that follow. Ideal matched filter signal
conditioning makes use of both amplitude and phase information in upgrading sig-
nal quality, and is implied in these SNR relationships for amplitude and phase error
in the case of random interference.
For practical applications the SNR requirements ascribed to amplitude and phase
error must be mathematically related to conventional amplifier and linear filter sig-
nal conditioning circuits. Figure 4-3 describes the basic signal conditioning struc-
ture, including a preconditioning amplifier and postconditioning filter and their
bandwidths. Earlier work by Fano [1] showed that under high-input SNR condi-
tions, linear filtering approaches matched filtering in its efficiency. Later work by
Budai [2] developed a relationship for this efficiency expressed by the characteris-
tic curve of Figure 4-4. This curve and its k parameter appears most reliable for fil-
ter numerical input SNR values between about 10 and 100, with an efficiency k of
0.9 for SNR values of 200 and greater.
Equations (4-10) through (4-13) describe the relationships upon which the im-
provement in signal quality may be determined. Both rms and dc voltage values
are interchangeable in equation (4-10). The Rcm and Rdiff impedances of the am-
plifier input termination account for the V 2/R transducer gain relationship of the
input SNR in equation (4-11). CMRR is squared in this equation in order to con-
vert its ratio of differential to common-mode voltage gains to a dimensionally cor-
rect power ratio. Equation (4-12) represents the processing–gain relationship for
the ratio of amplifier fhi to filter fc produced with the filter efficiency k, for im-
proving signal quality above that provided by the amplifier CMRR with random
interference. Most of the improvement is provided by the amplifier CMRR owing
to its squared factor, but random noise higher-frequency components are also ef-
fectively attenuated by linear filtering.

84 LINEAR SIGNAL CONDITIONING TO SIX-SIGMA CONFIDENCE
vided by equations (4-15) and (4-16), respectively, for coherent and random ampli-
tude error. Observe that these signal quality representations replace the Vcm/CMRR
entry in Table 2-4 when more comprehensive signal conditioning is employed.
Vcm Rdiff 1/2 AVcm fcoh 2n –1/2
coherent = · · · 1+ · 100% (4-15)
Vdiff Rcm AVdiff fc
Vcm Rdiff 1/2 AVcm 2 fc 1/2
random = · · · · 100% (4-16)
Vdiff Rcm AVdiff k fhi
4-3 DC, SINUSOIDAL, AND HARMONIC SIGNAL CONDITIONING
Signal conditioning is concerned with upgrading the quality of a signal to the accu-
racy of interest coincident with signal acquisition, scaling, and band-limiting. The
unique requirements of each analog data acquisition channel plus the economic
constraint of achieving only the performance necessary in specific applications are
an impediment to standardized designs. The purpose of this chapter therefore is to
develop a unified, quantitative design approach for signal acquisition and condi-
tioning that offers new understanding and accountability measures. The following
examples include both device and system errors in the evaluation of total signal
conditioning channel error.
A dc and sinusoidal signal conditioning channel is considered that has wide-
spread industrial application in process control and data logging systems. Tempera-
ture measurement employing a Type-C thermocouple is to be implemented over the
range of 0 to 1800 °C while attenuating ground conductive and electromagnetically
coupled interference. A 1 Hz signal bandwidth (BW) is coordinated with filter cut-
off to minimize the error provided by a single-pole filter as described in Table 3-5.
Narrowband signal conditioning is accordingly required for the differential-input
l7.2 V/°C thermocouple signal range of 0–3l mV dc, and for rejecting 1 V rms of
60 Hz common mode interference, providing a residual coherent error of
0.009%FS. An OP-07A subtractor instrumentation amplifier circuit combining a 22
Hz differential lag RC lowpass filter is capable of meeting these requirements, in-
cluding a full-scale output signal of 4.096 V dc with a differential gain AVdiff of 132,
without the cost of a separate active filter.
This austere dc and sinusoidal circuit is shown by Figure 4-5, with its parameters
and defined error performance tabulated in Tables 4-3 through 4-5. This AVdiff fur-
ther results in a –3dB frequency response of 4.5kHz to provide a sensor loop inter-
nal noise contribution of 4.4 Vpp with 100 ohms source resistance. With 1% toler-
ance resistors, the subtractor amplifier presents a common mode gain of 0.02 by the
considerations of Table 2-2. The OP-07A error budget of 0.103%FS is combined
with other channel error contributions including a mean filter error of 0.1%FS and
0.011%FS linearized thermocouple. The total channel error of 0.246%FS at 1 ex-
pressed in Table 4-5 is dominated by static mean error that is an inflexible error to

4-3 DC, SINUSOIDAL, AND HARMONIC SIGNAL CONDITIONING 87
be minimized throughout all instrumentation systems. Postconditioning lineariza-
tion software achieves a residual deviation from true temperature values of 0.2°C
over 1800°C, and active cold junction compensation of ambient temperature is pro-
vided by an AD590 sensor attached to the input terminal strip to within 0.5°C. Note
that Ri is 10 K ohms.
The information content of instrumentation signals is described by their amplitude
variation with time or, through Fourier transformation, by signal BW in Hz.
Instrumentation signal types are accordingly classified in Table 4-2, with their mini-
mum BW requirements specified in terms of signal waveform parameters. DC signal
time rate of change is equated to the time derivative of a sinusoidal signal evaluated
at its zero crossing to determine its BW requirement. In the case of harmonic signals,
a first-order rolloff of –20dB/decade is assumed from a full-scale signal amplitude at
the inverse waveform period 1/T, defining the fundamental frequency, declining to
one-tenth of full scale at a BW value of ten times the fundamental frequency.
Considered now is the premium harmonic signal conditioning channel of Figure
4-6, employing a 0.1%FS systematic error piezoresistive sensor that can transduce
acceleration signals in response to applied mechanical force. Postconditioning sig-
nal processing options include subsequent signal integration to obtain velocity and
then displacement vibration spectra from these acceleration signals by means of an
ac integrator, as shown in Figure 2-14, or by digital signal processing. A harmonic
signal spectral bandwidth is allowed for this example from dc to 1 KHz with the 1
K source resistance bridge sensor generating a maximum input signal amplitude of
70 mV rms, up to 100 Hz fundamental frequencies, with rolloff at –20db per decade
of frequency to 7 mV rms at 1 KHz BW. The ±0.5 V dc bipolar sensor excitation is
furnished by isolated three-terminal regulators to within ±50 V dc variation, pro-
viding a negligible 0.01%FS differential mode error. The sensor shield buffered
common-mode voltage active drive also preserves signal conditioning CMRR over
extended cable lengths.
An AD624C preamplifier raises the differential sensor signal to a ±5Vpp full-
scale value while attenuating 1 V rms of common mode random interference, in
concert with the lowpass filter, to a residual error of 0.006%FS, as defined by equa-
tion (4-16). The error budgets of the preamplifier and isolation amplifier, tabulated
in Tables 4-3 and 4-4, also include a sensor loop internal noise contribution of 15
Vpp based on the provisions of Figure 4-2, where the 1/f contact noise frequency is
taken as 10% of signal BW. Three contributions comprising this internal noise are
evaluated as source resistance thermal noise Vt, contact noise Vc arising from 1 mA
of dc current flow, and amplifier internal noise Vn. The three-pole Butterworth low-
pass filter cutoff frequency is derated to a value of 3 BW to minimize its device er-
ror. Note that the AD705 filter amplifier is included in the mean filter device error
of 0.115%FS. The total channel 1 instrumentation error of 0.221%FS consists of
an approximate equal sum of static mean and variable systematic error values at
one-sigma confidence in Table 4-5. Six-sigma confidence is defined by the extend-
ed value of 0.75%FS, consisting of one mean plus six RSS error values.